Finite element formulation for plate stability analysis

Structural stability of plate structure is an important issue in the design of many types of civil, mechanical, and aeronautical structures. Structural instability, in the form of bifurcation or a snap-through phenomenon, can be rigorously identified by tracing the nonlinear load-displacement paths of the structure. In this chapter the total Lagrangian formulation is presented to establish typical finite element expressions for the instability of Mindlin plates. Based on the rigorous formulation, the nonlinear deformation of the Mindlin plate prior to the elastic buckling limit is automatically included in the element stiffness matrices. The advantage of finite element method is its versatility and power in modelling any shape of thin and thick plates, even plates with nonuniform thickness. Although only two types of elements are illustrated in this chapter, the formulation is fully generic and shall be applicable to any Mindlin plate element.